Simulation of the nonlinear evolution of electron plasma waves

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Abstract
Electron plasma waves, commonly called Langmuir waves, are often observed upstream from planetary bow shocks and are widely accepted as being generated by electron beams. We have studied the self‐consistent nonlinear evolution of electron plasma waves excited by electron beams streaming along the ambient magnetic field in a long simulation system Lx = 2048λe. Only electrostatic waves are treated by the simulation code. The simulation results show the presence of a process moving wave energy from frequencies and wavenumbers predicted by linear theory to Langmuirlike frequencies during saturation of the instability. An explanation in terms of the characteristics of the growing waves changing with beam temperature is suggested. A decay process producing backward propagating (backscattered) Langmuirlike waves is observed. Low‐frequency waves are also produced. However, the simulation results indicate that the backscattering process is not the conventional Langmuir wave decay. Electrostatic waves near multiples of the electron plasma frequency are generated by wave‐wave coupling during the nonlinear stage of the simulations, thereby confirming the suggestions of Klimas (1983). However, the spectral width of the pumping waves and beam density are found to significantly affect the levels of harmonic waves. Care must therefore be taken to prevent unrealistically high levels of harmonic waves by including sufficient numbers of linearly unstable modes in the simulation system.